Don't do integrated brake/shifters. Separate brake levers and shifters would be the ticket. Lots of decent mountain bike pod shifters to choose from (I like the Deore stuff, durable and looks good and pretty cheap used) and then whatever canti/caliper brake levers you want to use.

As you have found out, most MTB integrated brake/shifter controls are v-brake except for older 7-8 speed stuff which had canti/caliper compatible levers back when canti brakes were more common.